These two remotes, by Apple (left, Apple TV) and Microsoft (right, Xbox 360), do approximately the same things with a few exceptions:

The Microsoft remote uses two AA batteries that need to be replaced about every 6 months. The Apple remote uses a single CR2032 that has never needed to be replaced.

The Apple remote has 6 buttons. The Microsoft remote has 46, only 15 of which are regularly used for media playback.

The buttons on the Microsoft remote are backlit so you can see what they do in the dark. The Apple remote doesn’t have this feature because you never need to look at the buttons after the first minute of use.

The Apple remote works from nearly any position in the room with approximate line-of-sight between itself and the front of the Apple TV. The Microsoft remote has the worst reception angle of any remote I’ve ever used (supposedly 90°, ±45°). Mine starts failing consistently at about 22° right of center at a distance of 8 feet, putting it right at the bottom of their specified total radius (~44°). It won’t even work from the right half of the couch.

This is a pretty good indicator of the two companies’ design philosophies and quality goals. And this isn’t even considering the software interface that each remote is respectively controlling.